A computer program to solve geometric programming problems: an illustration using Rijckaert and Martens' Problem 6 [76]
Jsun Yui Wong
Similar to the computer program of the preceding paper, the computer program listed below aims to solve the following geometric programming problem based on Problem 6 on page 229 of Rijckaert and Martens [76, p. 229]:
Minimize
- ( -2 * X(1) ^ .9 * X(2) ^ -1.5 * X(3) ^ -3 - 5 * X(4) ^ -.3 * X(5) ^ 2.6 - 4.7 * X(6) ^ -1.8 * X(7) ^ -.5 * X(8) )
subject to
7.2 * X(1) ^ -3.8 * X(2) ^ 2.2 * X(3) ^ 4.3 + .5 * X(4) ^ -.7 * X(5) ^ -1.6 + .2 * X(6) ^ 4.3 * X(7) ^ -1.9 * X(8) ^ 8.5 <= 1
10 * X(1) ^ 2.3 * X(2) ^ 1.7 * X(3) ^ 4.5 <= 1
.6 * X(4) ^ -2.1 * X(5) ^.4 <= 1
6.2 * X(6) ^ 4.5 * X(7) ^ -2.7 * X(8) ^ -.6 <= 1
3.1 * X(1) ^ 1.6 * X(2) ^ .4 *X(3) ^ -3.8 <= 1
3.7 * X(4) ^ 5.4 * X(5) ^ 1.3 <= 1
.3 * X(6) ^ -1.1 * X(7) ^ 7.3 * X(8) ^ -5.6 <= 1
.1 <= X(j) <= 10, j=1, ..., 8.
(The superscripts above can be clearer (less confusing) below:)
0 REM DEFDBL A-Z
1 REM DEFINT I, J, K
2 DIM B(99), N(99), A(2002), G(128), J44(222), H(99), L(99), U(99), X(2002), D(111), P(111), PS(33), J(99), AA(99), HR(32), HHR(32), LHS(44), PLHS(44), LB(22), UB(22), PX(44), PN(22), NN(22)
85 FOR JJJJ = -32000 TO 32000
87 RANDOMIZE JJJJ
88 M = -3D+30
107 FOR J44 = 1 TO 8
108 A(J44) = .1 + RND * 1
109 NEXT J44
128 FOR i = 1 TO 300000
129 FOR KKQQ = 1 TO 8
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
139 FOR IPP = 1 TO FIX(1 + RND * 8)
141 B = 1 + FIX(RND * 8)
142 IF RND < 1.5 THEN 160 ELSE GOTO 167
160 r = (1 - RND * 2) * A(B)
162 X(B) = A(B) + (RND ^ (RND * 15)) * r
164 GOTO 168
167 REM IF RND < .5 THEN X(B) = A(B) - 1 ELSE X(B) = A(B) + 1
168 NEXT IPP
171 REM X(5) = (1 / (.6 * X(4) ^ -2.1)) ^ 2.5
175 X(2) = (1 / (3.1 * X(1) ^ 1.6 * X(3) ^ -3.8)) ^ 2.5
176 X(6) = (1 / (6.2 * X(7) ^ -2.7 * X(8) ^ -.6)) ^ .222222222222
177 IF 3.7 * X(4) ^ 5.4 * X(5) ^ 1.3 > 1 THEN 1670
178 IF .6 * X(4) ^ -2.1 * X(5) ^ .4 > 1 THEN 1670
179 IF 10 * X(1) ^ 2.3 * X(2) ^ 1.7 * X(3) ^ 4.5 > 1 THEN 1670
205 IF .3 * X(6) ^ -1.1 * X(7) ^ 7.3 * X(8) ^ -5.6 > 1 THEN 1670
207 IF 7.2 * X(1) ^ -3.8 * X(2) ^ 2.2 * X(3) ^ 4.3 + .5 * X(4) ^ -.7 * X(5) ^ -1.6 + .2 * X(6) ^ 4.3 * X(7) ^ -1.9 * X(8) ^ 8.5 > 1 THEN 1670
431 FOR J44 = 1 TO 8
433 IF X(J44) < .1 THEN 1670
434 IF X(J44) > 10 THEN 1670
435 NEXT J44
967 PD1 = -2 * X(1) ^ .9 * X(2) ^ -1.5 * X(3) ^ -3 - 5 * X(4) ^ -.3 * X(5) ^ 2.6 - 4.7 * X(6) ^ -1.8 * X(7) ^ -.5 * X(8)
969 P = PD1
1111 IF P <= M THEN 1670
1452 M = P
1454 FOR KLX = 1 TO 8
1455 A(KLX) = X(KLX)
1456 NEXT KLX
1670 NEXT i
1777 IF M < -29.45 THEN 1999
1888 PRINT A(1), A(2), A(3), A(4), A(5), A(6), A(7), A(8), M, JJJJ
1999 NEXT JJJJ
This computer program was run with qb64v1000-win [102]. Its complete output of one run through JJJJ= -30163 is shown below:
.9817176 .193701 1.124328 .7938046 .9538843
.6856284 1.06237 .9398921 -29.42854 -30951
.9778123 .1950181 1.123243 .7898042 .9741132
.7035958 1.099447 .9778958 -29.32548 -30163
Above there is no rounding by hand; it is just straight copying by hand from the monitor screen. By using the following computer system and QB64v1000-win [102], the wall-clock time (not CPU time) for obtaining the output through JJJJ = -30163 was 35 minutes, counting from "Starting program...". One can compare the computational results above with those in Rijckaert and Martens [76, p. 229].
The computational results presented above were obtained from the following computer system:
Processor: Intel (R) Core (TM) i5 CPU M 430 @2.27 GHz 2.26 GHz
Installed memory (RAM): 4.00GB (3.87 GB usable)
System type: 64-bit Operating System.
Acknowledgement
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
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